Dynamics and Topology of Non-Hermitian Elastic Lattices with Non-Local Feedback Interactions

We investigate a family of non-Hermitian 1D elastic lattices whereby feedback control is used to establish non-local, non-reciprocal strain based interactions. We demonstrate that wave propagation is largely non-reciprocal for all frequencies within the dispersion bands, manifesting as either gain or loss for opposite propagation directions. The non-reciprocal bands are tunable based on the non-local interactions, which can define multiple frequency bands with opposite non-reciprocal behavior. The large non-reciprocity also manifests in finite lattices whereby all the bulk eigenmodes are localized at a boundary, which is known as the non-Hermitian skin effect. In analogy to recent work in quantum lattices, we show that the winding numbers of the dispersion bands on the complex plane predict the localization edge of the skin modes of finite lattices, which can be interpreted as a bulk-bulk correspondence principle. Finally, we investigate wave propagation in 2D lattices where directional non-reciprocity is demonstrated, and show preliminary results that suggest a 2D manifestation of the non-Hermitian skin effect in the form of corner modes for finite lattices.